WASHINGTON — The backbone of America’s financial system is only as strong as the next tweet.

A bogus post on Twitter yesterday — sent by Syrian hackers who took over The Associated Press’ account and reported “explosions” at the White House — set off a panic that sent the Dow Jones industrial average plunging 146 points in about three minutes, erasing some $42 billion.

The fake tweet was debunked, and the market quickly rebounded, gaining 137 points, only 9 points away from where it was before the post was sent.

A group called the Syrian Electronic Army, which supports dictator Bashar al-Assad, took responsibility for the hack job.

It was also odd for any initial report of explosions — which would have been audible to hundreds of people — to contain an instant health update on the president.

“Oops! @AP get owned by Syrian Electronic Army!” the group wrote — posting a link to a screenshot of the AP’s Web site with the false tweet.

The group has previously boasted about hacking into the accounts of CBS, “60 Minutes,” BBC Weather, Columbia University and National Public Radio.

“The American people have been lied to by their media about Syria,” the group wrote on the “60 Minutes” site.

Yesterday’s drama began unfolding at 1:07 p.m.

“If you needed evidence that traders watch Twitter, that was it. Dow tanked in moments on single hacked tweet,” CNBC anchor Brian Sullivan posted on the social-media site.

The fake tweet went out to AP’s 1.9 million followers, carrying the news agency’s official symbol and reading: “Two Explosions in the White House and Barack Obama is injured.”

That language set off computer programs that immediately began selling stock.

“These high-frequency trading algorithms, they see something fall a certain amount, and that kicks in the program. It’s like an aircraft that has automatic stabilizers,” said David Darst, chief investment strategist for Morgan Stanley.

The drop was nearly 1 percent of the Dow’s $4.33 trillion value.

“We’re working with Twitter to sort this out,” AP spokesman Paul Colford told The Post. “We’ve suspended other Twitter accounts out of a sense of caution.”

The FBI is investigating the hack. An AP reporter apologized for the breach at the start of White House Press Secretary Jay Carney’s daily press briefing, calling the report “absolutely false.”

“The president is fine. I was just with him,” Carney said.

After the situation was cleared up, the Dow ended 152 points up for the day.

Meanwhile, there were immediate clues that the tweet was fake. It didn’t refer to Obama by his official title of “president,” and it never went out on the official AP news wire to subscribers.

The AP said the attack was preceded by a “phishing attempt” on its corporate network — a tactic that sends employees an e-mail that steers them to a fake Web site in order to glean information.

“Secret Service is aware of the incident and will monitor and conduct appropriate follow-up,” said spokesman Brian Leary.

Uncovering the culprit could be difficult.

“It can be hard to figure out who is pulling the strings,” said John Pike, of Global Security.org.

“I don’t necessarily think of Syria as being a leading light in information warfare.”